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**Unformatted text preview: **striction
on k −1 means we take the right half of the parabola.
y
2
y = k(x) 1 −2 −1 1
−1 2 x y = k−1 (x) −2 Our last example of the section gives an application of inverse functions.
Example 5.2.4. Recall from Section 2.1 that the price-demand equation for the PortaBoy game
system is p(x) = −1.5x + 250 for 0 ≤ x ≤ 166, where x represents the number of systems sold
weekly and p is the price per system in dollars.
1. Explain why p is one-to-one and ﬁnd a formula for p−1 (x). State the restricted domain.
2. Find and interpret p−1 (220).
3. Recall from Section 2.3 that the weekly proﬁt P , in dollars, as a result of selling x systems is
given by P (x) = −1.5x2 + 170x − 150. Find and interpret P ◦ p−1 (x). 308 Further Topics in Functions 4. Use your answer to part 3 to determine the price per PortaBoy which would yield the maximum proﬁt. Compare with Example 2.3.3.
Solution.
1. We leave to the reader to show the graph of p(x) = −1.5x + 250, 0 ≤ x ≤ 166, is a line
segment from (0, 250) to (166, 1), and as such passes the Horizontal Line Test. Hence, p is
−
one-to-one. We ﬁnd the expression for p−1 (x)...

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